DLMF:5.4.E20 (Q2058)

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DLMF:5.4.E20
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    Statements

    Defining formula
    x n = - n + 1 π ⁢ arctan ⁡ ( π ln ⁡ n ) + O ⁡ ( 1 n ⁢ ( ln ⁡ n ) 2 ) . subscript 𝑥 𝑛 𝑛 1 𝜋 𝜋 𝑛 Big-O 1 𝑛 superscript 𝑛 2 {\displaystyle{\displaystyle x_{n}=-n+\frac{1}{\pi}\operatorname{arctan}\left(% \frac{\pi}{\ln n}\right)+O\left(\frac{1}{n(\ln n)^{2}}\right).}}
    0 references
    DLMF id
    DLMF:5.4.E20
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
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    Q10816
    Defining formula
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7adec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
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    Q11274
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C5.S1.XMD3.m1edec
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    Q11281
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C5.S1.XMD5.m1adec
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